Question

Areas in the plane

Answer 1

Cool.

Answer 2

The first question. Number 13 :(

Answer 3

Find two areas separately.

Answer 4

yes but I get confused on putting the limits for integration. And is it better to integrate in terms of y?

Answer 5

y? You are crazy! Integrating in term of x is MUCH easier. Don't see what it has to do with limit, but you can just set up a integration like this:
\[\int_{-2}^{0}(2x^3 -x^2 -5x) - (-x^2+3x)dx + \int_0^2 (-x^2+3x) - (2x^3-x^2-5x)dx\]
See what I did here?

Answer 6

oh ok. it's because integrating with y is easier with some areas. I don't know exactly when to integrate with y and x

Answer 7

Well, if functions are used, then just use x. If at least one of the curve don't pass vertical test, then it is better to use y.